In the LieAlgebras package, the command DGsetup is used to initialize a Lie algebra -- that is, to define the basis elements for the Lie algebra and its dual and to store the structure constants for the Lie algebra in memory.  The first argument for DGsetup is a Lie algebra data structure which contains the structure constants in a standard format used by the LieAlgebras package.

Let h be a subalgebra of a Lie algebra g.  The command LieAlgebraData(Subalgebra) will return the Lie data structure for the subalgebra h which can then be initialized.  In this way the subalgebra h can be studied as a Lie algebra in its own right, independent of the original ambient algebra g.

Let h be a subalgebra of a Lie algebra g.  With the optional argument "Matrix", LieAlgebraData(Subalgebra, "Matrix") will return the Lie data structure for the subalgebra h and a Matrix which defines the inclusion map from the subalgebra h to the Lie algebra g.

Let k1, k2, ... be subalgebras of h (and hence subalgebras of g).  The command LieAlgebraData(Subalgebra, SubSubalgebras) will return the Lie algebra data structure for the subalgebra h and the list of lists of components for the vectors in k1, k2, ... with respect to the given basis for the subalgebra h.  With this information and the DGzip program, k1, k2, ... can then be converted to subalgebras of the Lie algebra obtained from h.

The command LieAlgebraData is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form LieAlgebraData(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-LieAlgebraData(...).